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| | Prerequisite: Satisfactory performance on a placement examination. This course is designed to prepare the student for [[MAT1093]] Precalculus and [[MAT1214]] Calculus I. Topics may include algebraic expressions; equations; inequalities over the real numbers; relations; functions; polynomial and rational functions; logarithmic and exponential functions; systems of linear equations and inequalities; matrices and determinants; complex numbers; sequences; series binomial expansion; mathematical induction; permutations, and combinations. (Formerly MTC 1073. Credit can be earned for only one of the following: MAT 1073, MTC 1073, [[MAT1063]], MTC 1023, or [[MAT1023]]. NOTE: For the purpose of the Three-Attempt Rule, these courses are considered to be equivalent and additional fees may be charged for the third or subsequent attempt to take any of these courses in any combination.) May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: LRC1 $12; LRS1 $45; STSI $21. | | Prerequisite: Satisfactory performance on a placement examination. This course is designed to prepare the student for [[MAT1093]] Precalculus and [[MAT1214]] Calculus I. Topics may include algebraic expressions; equations; inequalities over the real numbers; relations; functions; polynomial and rational functions; logarithmic and exponential functions; systems of linear equations and inequalities; matrices and determinants; complex numbers; sequences; series binomial expansion; mathematical induction; permutations, and combinations. (Formerly MTC 1073. Credit can be earned for only one of the following: MAT 1073, MTC 1073, [[MAT1063]], MTC 1023, or [[MAT1023]]. NOTE: For the purpose of the Three-Attempt Rule, these courses are considered to be equivalent and additional fees may be charged for the third or subsequent attempt to take any of these courses in any combination.) May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: LRC1 $12; LRS1 $45; STSI $21. |
| | | | |
| − | ==Topics List==
| + | {| class="wikitable" |
| − | {| class="wikitable sortable" | + | ! Week !! Topics !! Prerequisite Skills !! Student Learning Outcomes |
| − | ! Week !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes | |
| − | |-
| |
| − | |Week 1
| |
| − | ||
| |
| − | Fundamentals
| |
| − | ||
| |
| − | * [[Algebraic Properties]]
| |
| − | ||
| |
| − | * Basic mathematical symbols and terminology
| |
| − | * Basic arithmetic skills
| |
| − | | |
| − | ||
| |
| − | Students will be able to correctly identify the algebraic properties:
| |
| − | * Additive & Multiplicative identity
| |
| − | * Additive & Multiplicative inverse
| |
| − | * Commutative property
| |
| − | * Associative property
| |
| − | * Distributive property
| |
| − | | |
| − | | |
| − | Students will be able to correctly explain the algebraic properties of numbers and correctly apply these properties in procedural explanations of:
| |
| − | * Solving mathematical equations
| |
| − | * Simplifying/evaluating mathematical expressions
| |
| | |- | | |- |
| − | |Week 2 | + | | Week 1 || Propositional logic: Axioms and Rules of Inference. Boolean Algebras. Limitations of propositional logic: Informal introduction to quantifiers and syllogisms. || || |
| − | || | |
| − | Fundamentals
| |
| − | ||
| |
| − | * [[Fractions]]
| |
| − | ||
| |
| − | * Basic mathematical symbols and terminology
| |
| − | * Basic arithmetic skills
| |
| − | * Basic understanding of [[Algebraic Properties]]
| |
| − | | |
| − | | |
| − | ||
| |
| − | Students will be able to add, subtract fractions:
| |
| − | * Determine common denominators and equivalent fractions
| |
| − | * Work with proper and improper fractions
| |
| − | * Simplify to lowest terms
| |
| − | | |
| − | Students will be able to multiply, and divide fractions:
| |
| − | * Work with proper and improper fractions
| |
| − | * Simplify to lowest terms
| |
| − | | |
| | |- | | |- |
| − | |Week 2 | + | | Week 2 || Predicate Logic: Existential and universal quantification, free variables and substitutions. Discussion of the various axiomatic systems for first-order logic (including axioms and rules of inference). The power and the limitations of axiomatic systems for logic: Informal discussion of the completeness and incompleteness theorems. || || |
| − | || | |
| − | Fundamentals
| |
| − | ||
| |
| − | * [[Factoring]]
| |
| − | ||
| |
| − | * Basic mathematical symbols and terminology
| |
| − | * Basic arithmetic skills
| |
| − | * Basic understanding of [[Algebraic Properties]]
| |
| − | | |
| − | | |
| − | ||
| |
| − | Students will be able to:
| |
| − | * Identify factored vs non-factored forms of a polynomial
| |
| − | * Successfully factor binomials & trinomials and difference of squares into two binomial terms
| |
| − | * Factor out GCF
| |
| − | * Multiply and / or distribute to check their factors are correct
| |
| − | * Differentiate between factors and terms of a polynomial expression
| |
| − | | |
| | |- | | |- |
| − | |Week 3 | + | | Week 2 || Sets: Operations on sets. Correspondence between finitary set operations and propositional logic. Correspondence between infinitary operations and quantifiers. The power and limitations of the language of set theory: Informal discussion of the set-theoretic paradoxes and the need for axiomatic systems for set theory. || || |
| − | || | |
| − | Module 1.1
| |
| − | ||
| |
| − | * [[Linear Equations]]
| |
| − | ||
| |
| − | * Basic mathematical symbols and terminology
| |
| − | * Basic arithmetic skills
| |
| − | * Basic understanding of [[Algebraic Properties]]
| |
| − | * Understanding of the Cartesian coordinate system
| |
| − | | |
| − | || | |
| − | Students will be able to:
| |
| − | * Solving linear equations in one variable
| |
| − | * Determine a linear equation
| |
| − | * Write and interpret a linear equation
| |
| − | * Graph a linear equation
| |
| | |- | | |- |
| − | |Week 3 | + | | Week 3 || Relations: Properties of relations. Special relations: Equivalence relations, partially ordered sets, totally ordered sets. || || |
| − | || | |
| − | Module 1.2
| |
| − | ||
| |
| − | * [[Systems of Equations in Two Variables]]
| |
| − | || | |
| − | * Basic mathematical symbols and terminology
| |
| − | * Basic arithmetic skills
| |
| − | * Basic understanding of [[Algebraic Properties]]
| |
| − | * Basic understanding of [[Linear Equations]] (Module 1.1)
| |
| − | || | |
| − | Students will be able to:
| |
| − | * Solve systems of equations by graphing.
| |
| − | * Solve systems of equations by substitution.
| |
| − | * Solve systems of equations by elimination
| |
| − | * Identify inconsistent systems of equations containing two variables.
| |
| − | * Express the solution of a system of dependent equations containing two variables.
| |
| | |- | | |- |
| − | |Week 4 | + | | Week 3 || Functions: Operations of functions, direct image and inverse image. || || |
| − | || | |
| − | Module 2.1
| |
| − | ||
| |
| − | * [[Functions]]
| |
| − | || | |
| − | * Basic understanding of [[Linear Equations]] (Module 0.4)
| |
| − | || | |
| − | Students will be able to:
| |
| − | * Determine whether a relation represents a function.
| |
| | |- | | |- |
| − | |Week 4 | + | | Week 4 || Well-ordered sets: Correspondence between well-ordering relations and induction. Correspondence between well-ordering relations and choice functions. (6) Introduction to computability. Classical models of computation (recursive functions, and Turing models). || || |
| − | || | |
| − | Module 2.2
| |
| − | ||
| |
| − | * [[Function Notation]]
| |
| − | ||
| |
| − | * Basic understanding of [[Functions]] (Module 2.1)
| |
| − | ||
| |
| − | Students will be able to:
| |
| − | * Find the value of a [[Functions]]
| |
| − | * Graph the functions listed in the library of functions.
| |
| − | * Determine whether a function is one-to-one.
| |
| − | * Use the vertical line test to identify functions.
| |
| | |- | | |- |
| − | |Week 4 | + | | Week 4 || Limitations of computation. Contemporary models of computation: Digital vs analog vs quantum computing. || || |
| − | || | |
| − | Module 2.2
| |
| − | ||
| |
| − | * [[Domain of a Function]]
| |
| − | ||
| |
| − | * An understanding of [[Function Notation]]
| |
| − | ||
| |
| − | Students will be able to:
| |
| − | * Find the domain of a function defined by an equation.
| |
| − | | |
| − | |-
| |
| − | |Week 4
| |
| − | ||
| |
| − | Module 2.2
| |
| − | ||
| |
| − | * [[Range of a Function]]
| |
| − | ||
| |
| − | * An understanding of [[Function Notation]]
| |
| − | ||
| |
| − | Students will be able to:
| |
| − | * Find the range of a function defined by an equation.
| |
| − | |-
| |
| − | |Week 4
| |
| − | ||
| |
| − | Module 2.2
| |
| − | ||
| |
| − | * [[Toolkit Functions]]
| |
| − | ||
| |
| − | * Basic understanding of [[Functions]] (Module 2.1)
| |
| − | ||
| |
| − | Students will be able to:
| |
| − | * Identify the basic toolkit functions
| |
| − | * Determine [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for the basic toolkit functions (Module 2.2)
| |
| − | | |
| − | |-
| |
| − | |Week 5
| |
| − | ||
| |
| − | Module 3.1
| |
| − | ||
| |
| − | * [[Composition of Functions]]
| |
| − | ||
| |
| − | * Basic understanding of [[Functions]] (Module 2.1)
| |
| − | * Basic understanding of [[Function Notation]] (Module 2.2)
| |
| − | * Basic understanding of [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.2)
| |
| − | ||
| |
| − | Students will be able to:
| |
| − | * Combine functions using [[Algebraic Properties]]
| |
| − | * Create a new function by composition of functions
| |
| − | * Evaluate composite functions
| |
| − | * Find the domain of a composite function
| |
| − | * Decompose a composite function into its component functions
| |
| − | |-
| |
| − | |Week 5
| |
| − | ||
| |
| − | Module 3.2
| |
| − | ||
| |
| − | * [[Inverse Functions]]
| |
| − | ||
| |
| − | * Basic understanding of [[Functions]] (Module 2.1)
| |
| − | * Basic understanding of [[Function Notation]] (Module 2.2)
| |
| − | * Basic understanding of [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.2)
| |
| − | * Basic understanding of [[Composition of Functions]] (Module 3.1)
| |
| − | ||
| |
| − | Students will be to able to:
| |
| − | * Verify inverse functions using [[Algebraic Properties]]
| |
| − | * Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one
| |
| − | * Find or evaluate the inverse of a function
| |
| − | * Use the graph of a one-to-one function to graph its inverse function on the same axes
| |
| − | | |
| − | |-
| |
| − | |Week 6
| |
| − | ||
| |
| − | Module 4.1
| |
| − | ||
| |
| − | * [[Exponential Properties]]
| |
| − | ||
| |
| − | * Basic mathematical symbols and terminology
| |
| − | * Basic arithmetic skills
| |
| − | * Basic understanding of [[Algebraic Properties]]
| |
| − | ||
| |
| − | Students will be able to:
| |
| − | * Use the product rule for exponents.
| |
| − | * Use the quotient rule for exponents.
| |
| − | * Use the power rule for exponents.
| |
| − | |-
| |
| − | |Week 6
| |
| − | ||
| |
| − | Module 4.2
| |
| − | ||
| |
| − | * [[Exponential Functions]]
| |
| − | ||
| |
| − | * Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] of the [[Toolkit Functions]] for exponential functions (Module 2.2)
| |
| − | * Basic understanding of [[Exponential Properties]] (Module 4.1)
| |
| − | ||
| |
| − | Students will be able to:
| |
| − | * Determine the difference between [[Linear Equations|Linear]] and Exponential Functions (Module 1.1)
| |
| − | * Evaluate exponential functions.
| |
| − | * Find the equation of an exponential function.
| |
| − | * Evaluate exponential functions with base e.
| |
| − | * Evaluate exponential functions with base 10.
| |
| − | * Graph exponential functions.
| |
| − | | |
| − | |-
| |
| − | |Week 7
| |
| − | ||
| |
| − | Module 5.1
| |
| − | ||
| |
| − | * [[Logarithmic Properties]]
| |
| − | ||
| |
| − | * Basic understanding of [[Exponential Properties]] (Module 4.1)
| |
| − | ||
| |
| − | Students will be to able:
| |
| − | * Rewriting from exponential form to logarithmic form and vice versa
| |
| − | :-y=b^x\equiv\log_b(y)=x
| |
| − | * Use the product rule for logarithms.
| |
| − | * Use the quotient rule for logarithms.
| |
| − | * Use the power rule for logarithms.
| |
| − | * Expand logarithmic expressions.
| |
| − | * Condense logarithmic expressions.
| |
| − | * Use the change-of-base formula for logarithms.
| |
| − | | |
| − | |-
| |
| − | |Week 7
| |
| − | ||
| |
| − | Module 5.2
| |
| − | ||
| |
| − | * [[Logarithmic Functions]]
| |
| − | ||
| |
| − | * Basic understanding of [[Inverse Functions]] (Module 3.2)
| |
| − | * Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] of [[Toolkit Functions]] for logarithmic functions. (Module 2.2)
| |
| − | * Basic understanding of [[Exponential Properties]] (Module 4.1)
| |
| − | | |
| − | ||
| |
| − | Students will be able to:
| |
| − | * Evaluate logarithms.
| |
| − | * Use common logarithms.
| |
| − | * Use natural logarithms.
| |
| − | * Graph logarithmic functions.
| |
| − | | |
| − | |-
| |
| − | |Week 8
| |
| − | ||
| |
| − | Module 6.2
| |
| − | ||
| |
| − | * [[Quadratic Equations]]
| |
| − | ||
| |
| − | * Basic arithmetic skills
| |
| − | * Basic understanding of [[Algebraic Properties]]
| |
| − | * Basic understanding of [[Factoring]]
| |
| − | ||
| |
| − | Students will be able to:
| |
| − | * Determine complex number solutions
| |
| − | * Determine solutions of quadratic equations using factoring techniques
| |
| − | * Determine solutions of quadratic equations using Quadratic Formula
| |
| − | | |
| − | |-
| |
| − | |Week 8
| |
| − | ||
| |
| − | Module 6.2
| |
| − | ||
| |
| − | * [[Quadratic Functions]]
| |
| − | ||
| |
| − | * Basic understanding of [[Quadratic Equations]]
| |
| − | | |
| − | ||
| |
| − | Students will be able to:
| |
| − | * Basic understanding of a polynomial expression.
| |
| − | * Recognize characteristics of parabolas
| |
| − | * Understand how the graph of a parabola is related to its quadratic function
| |
| − | * Determine a quadratic function's minimum or maximum value
| |
| − | * Solve problems involving a quadratic function's minimum or maximum value
| |
| − | | |
| − | | |
| − | |-
| |
| − | |Week 9
| |
| − | ||
| |
| − | Module 7.1
| |
| − | ||
| |
| − | * [[Dividing Polynomials]]
| |
| − | ||
| |
| − | * Basic understanding of [[Fractions]] (Fundamentals)
| |
| − | * Basic understanding of [[Factoring]] (Fundamentals)
| |
| − | * The student recalls the graphs and equations of [[Toolkit Functions]], and their associated [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.2)
| |
| − | * Basic understanding of [[Quadratic Functions]] (Module 6.2)
| |
| − | | |
| − | || | |
| − | Students will be able to:
| |
| − | * Identify polynomial functions.
| |
| − | * Identify the degree and leading coefficients of polynomial functions.
| |
| − | * Use long division to divide polynomials
| |
| − | * Use synthetic division to divide polynomials
| |
| − | |-
| |
| − | |Week 9
| |
| − | ||
| |
| − | Module 7.2
| |
| − | ||
| |
| − | * [[Factoring Polynomials|Zeros of Polynomials]]
| |
| − | ||
| |
| − | * Basic understanding of [[Fractions]] (Fundamentals)
| |
| − | * Basic understanding of [[Functions]] (Module 2.1)
| |
| − | * Basic understanding of [[Dividing Polynomials]] (Module 7.1)
| |
| − | ||
| |
| − | Students will be able to:
| |
| − | * Evaluate a polynomial using the Remainder Theorem
| |
| − | * Use the Factor Theorem to solve a polynomial equation
| |
| − | * Use the Rational Zero Theorem to find rational zeros
| |
| − | * Find zeros of a polynomial function
| |
| − | * Solve real-world applications of polynomial equations
| |
| − | | |
| − | |-
| |
| − | |Week 10
| |
| − | ||
| |
| − | Module 8.1
| |
| − | ||
| |
| − | * [[Power and Polynomial Functions]]
| |
| − | ||
| |
| − | * Basic understanding of [[Factoring]] (Fundamentals)
| |
| − | * Basic understanding of [[Quadratic Functions]] (Module 6.2)
| |
| − | * Basic understanding of [[Dividing Polynomials]] (Module 7.1)
| |
| − | * Basic understanding of [[Factoring Polynomials|Zeros of Polynomials]] (Module 7.2)
| |
| − | ||
| |
| − | Students will be able to:
| |
| − | * Find the average rate of change of a function.
| |
| − | * Use a graph to determine where a function is increasing, decreasing, or constant.
| |
| − | * Use a graph to locate local maxima and local minima.
| |
| − | * Use a graph to locate the absolute maximum and absolute minimum.
| |
| − | * Identify end behavior of power functions.
| |
| − | | |
| − | | |
| − | | |
| − | |-
| |
| − | |Week 10
| |
| − | ||
| |
| − | Module 8.2
| |
| − | ||
| |
| − | * [[Graphs of Polynomials]]
| |
| − | ||
| |
| − | * Basic understanding of [[Dividing Polynomials]] (Module 7.1)
| |
| − | * Basic understanding of [[Factoring Polynomials|Zeros of Polynomials]] (Module 7.2)
| |
| − | ||
| |
| − | Students will be able to:
| |
| − | * Recognize characteristics of graphs of polynomial functions
| |
| − | * Use [[Factoring]] to find zeros of polynomial functions
| |
| − | * Identify zeros and their multiplicities
| |
| − | * Determine end behavior of polynomial functions
| |
| − | * Understand the relationship between degree and turning points
| |
| − | * Graph polynomial functions
| |
| − | | |
| − | |-
| |
| − | |Week 11
| |
| − | ||
| |
| − | Module 9.1
| |
| − | ||
| |
| − | * [[Rational Expressions]]
| |
| − | ||
| |
| − | * The student understands that zero in the denominator of a fraction is undefined.
| |
| − | * Basic understanding of [[Fractions]] (Fundamentals)
| |
| − | ||
| |
| − | Students will be able to:
| |
| − | * Simplify rational expressions.
| |
| − | * Multiply rational expressions.
| |
| − | * Divide rational expressions.
| |
| − | * Add and subtract rational expressions.
| |
| − | | |
| − | |-
| |
| − | |Week 11
| |
| − | ||
| |
| − | Module 9.2
| |
| − | ||
| |
| − | * [[Graphs of Rational Functions]]
| |
| − | ||
| |
| − | * Basic understanding of [[Rational Expressions]] (Module 9.1)
| |
| − | ||
| |
| − | Students will be able to:
| |
| − | * Identify and graph vertical asymptotes
| |
| − | * Identify and graph horizontal asymptotes
| |
| − | * Determine behavior of rational functions around vertical asymptotes
| |
| − | * Find the domains of rational functions
| |
| − | * Graph rational functions
| |
| − | | |
| − | |-
| |
| − | |Week 12
| |
| − | ||
| |
| − | Module 10.1
| |
| − | ||
| |
| − | * [[Single Transformations of Functions]]
| |
| − | ||
| |
| − | * Understanding of [[Function Notation]] (Module 2.1)
| |
| − | ||
| |
| − | Students will be able to:
| |
| − | * Graph functions using vertical and horizontal shifts
| |
| − | * Graph functions using reflections about the x-axis and the y-axis
| |
| − | | |
| − | |-
| |
| − | |Week 12
| |
| − | ||
| |
| − | Module 10.2
| |
| − | ||
| |
| − | * [[Multiple Transformations of Functions]]
| |
| − | ||
| |
| − | * Understanding of [[Single Transformations of Functions]] (Module 10.1)
| |
| − | ||
| |
| − | Students will be able to:
| |
| − | * Determine whether a function is even, odd, or neither
| |
| − | * Graph functions using compressions and stretches
| |
| − | * Combine transformations
| |
| − | | |
| − | | |
| − | | |
| | |} | | |} |
